math help

What is 3/9 - 8/12?

What is 3/9 - 8/12?

Here's how to subtract 8/12 from 3/9:

3
9
8
12

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 3 by 12, and get 36.

Then we multiply 8 by 9, and get 72.

Next we give both terms new denominators -- 9 × 12 = 108.

So now our fractions look like this:

36
108
72
108

Step 2

Since our denominators match, we can subtract the numerators.

36 − 72 = -36

So the answer is:

-36
108

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

-36
108
÷ 2 =
-18
54

Let's try dividing by 2 again...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

-18
54
÷ 2 =
-9
27

Let's try dividing by 2 again...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

-9
27
÷ 3 =
-3
9

Let's try dividing by 3 again...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

-3
9
÷ 3 =
-1
3

Let's try dividing by 3 again...

No good. 3 is larger than -1. So we're done reducing.

There you have it! The final answer is:
3
9
8
12
=
1
3